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How to prove A or C from premises A or B and -B or C. Am using fitch and have been stuck on this for an hour

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  • What did you try? – Graham Kemp Aug 19 '20 at 3:42
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Our goal is a disjunction. Working forward (from the premises) seems a good option. As A v B and ¬B v C both have a disjunction as its main logical connective, we will attempt to use Disjunction Elimination rule. The proof skeleton, would be:

1.  | A v B
2.  |_ ¬B v C
3.  | |_ A
4.  | | A v C       v Intro: 3
5.  | |_ B
6.  | | |_ ¬B
7.  | | | ⊥        ⊥ Intro: 6,5
8.  | | | ...
9.  | | |_ C
10. | | | ...
11. | | ...
12. | A v C         v Elim: 3-4, 5-11

Can you complete the proof, now ?

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  1. (A v B)
  2. -(B v C)
  3.         | A___        ASSUME
  4.         | (A v C)     [v-introduction, 3]
  5.         | B___       ASSUME
  6.            | -B___    ASSUME
  7.            | ⊥           [⊥-introduction, 5,6]
  8.            | (A v C)   [⊥-elimination, 7]
  9.            | C___     ASSUME
  10.            | (A v C)   [v-introduction, 9]
  11.         | (A v C)      [v-elimination, 2, 6-8, 9-10]
  12. (A v C)                [v-elimination, 1, 3-4, 5-11]

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